What is the general solution for 2cos(x)-cos(x)sin(x)=0 ?

The general solution for 2cos(x)-cos(x)sin(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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2cos(x)-cos(x)sin(x)=0

2 cos (x) - cos (x) sin (x) = 0

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

2 cos (x) - cos (x) sin (x) = 0

Factor

2 cos (x) - cos (x) sin (x) : - cos (x) (sin (x) - 2)

- cos (x) (sin (x) - 2) = 0

Solving each part separately

cos (x) = 0 or sin (x) - 2 = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

sin (x) - 2 = 0 :

No Solution

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

10 sin (x) - 7 = 0

2 tan^{3} (x) - 6 tan (x) = 0, 0 \leq x \leq π

5 cos (x) = 5 cos (2 x)

cos (4 θ) = cos (2 θ)

3 cos (3 x) = 2

What is the general solution for 2cos(x)-cos(x)sin(x)=0 ?
The general solution for 2cos(x)-cos(x)sin(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin